Delegates of the 1787 Constituti.......... Cool math question! Check it out!?

Question

Delegates of the 1787 Constitutional Convention established the framework for the United States Senate to include two senators from each of the U. S. states. Today, there are 100 senators. If a new five-member committee on mathematics education is to be created but no state represented by more than one senator, in how many ways can this new committee be formed?

Best answer will be given to the first correct answer that explains why there answer is correct ( Like showing your work).

Answer 1

First choose a state, then choose one of two senators, do this 5 times.

50C5 to get the states

there are two choices for each of these

so, I think that it's
2^5(50C5) = 67,800,320

bgood's analysis preserves order, which I don't think is important here.

Added:

Actually, I needed to add a factor of 2^5 to my answer, and bgood needs to divide by 5! to take out order and then both our answers should be the same!

bgood: 8,136,038,400/5! = 67,800,320

so, our answers agree

Answer 2

attempt forgetting with regard to the maths for a 2d and think of of with regard to the superb judgment. The congress is a great physique geared up from many individuals. Democracy is all approximately technique. The Founders understood that how we attain a result concerns. As congressional scholar Norman Ornstein those days stated, “The device of exams and balances and the legislative technique because of the fact it more desirable in the homestead and the Senate have been geared up around deliberation... If there is one be conscious on the middle of Congress’ essence, that's deliberation.” The Founders created a device to examine that anybody proposals acquire cautious scrutiny, and that anybody voices are viewed, no longer in basic terms a slim majority. If those on the dropping end don’t see the technique as open and difficulty-free, they modify into disgruntled, uncooperative, and finally vindictive, and our democracy suffers. I even have a perplexing time believing the technique isn't greater beneficial important than the maths. Congress is a deliberative physique, and that they understand the finished worldwide is gazing. Do you particularly have self assurance that's a threat that they could scotch the finished deal on the ultimate minute? enable's incredibly instruct the worldwide what a wishy-washy physique we are, how we are announcing one element and do yet yet another on the very very final minute. incredibly various the Clinton great delegates have switched aspects to Obama in spite of the incontrovertible fact that the alternative isn't easily. no person has deserted Obama's advertising campaign to connect Hillary. a impressive replace on the ultimate minute ought to seem greater beneficial like a coup d’état, than democracy. that's over. Do you recognize?

Answer 3

100 * 98 * 96 * 94 * 92 = 8,136,038,400
You choose one Senator from a pool of 100, say Hillary Clinton. Both she and Chuck Schumer our out, so you have 98 left to choose from. Let's pick John McCain, so both he and the other AZ Senator are out, and you have 96 left. And so on.